I\'m trying to find a list of strings that can be used a a crypto algorithm to fit into this function, replacing SHA256.
crypto.cre
SHA-256 is not a cipher, it is a hash algorithm. That is probably why you didn't find it in a list of ciphers. The same goes for MD5 and all the various SHA algorithms.
Indeed, a hash algorithm is exactly what you need for HMAC. If you want to construct a MAC based on a block cipher, you'll need to use some other construction, such as OMAC/CMAC, PMAC or CBC-MAC.